Convex functions play an important role in almost all branches of mathematics, and this book is a thorough introduction to contemporary convex function theory. It covers a large variety of subjects, from the one real variable case (with all its mathematical gems) to some of the most advanced topics such as Choquet's theory, the Prékopa-Leindler type inequalities and their ramifications, as well as the variational approach of partial differential equations and convex programming.
Rezensionen / Stimmen
From the reviews:
"This monograph is aimed to serve as an elementary graduate textbook on convex functions. . Four appendices complete this book. . A list of exercises is provided at the end of each section. Every chapter is closed by a section with valuable historical remarks and comments on further developments." (Giovanni Alberti, Mathematical Reviews, Issue 2006 m)
"The book is devoted to elementary theory of convex functions. . The book will be useful to all who are interested in convex functions and their applications." (Peter Zabreiko, Zentralblatt MATH, Vol. 1100 (2), 2007)
"This is a nice little book, providing a new look at the old subject of convexity and treating it from different points of view. As the authors suggest, parts of it can be used for a course on convexity for first year graduate students. . The book well documents sources of ideas and the origins of results and will be of interest even for specialists in the field; it may also be used as a reference book on the subject." (EMS Newsletter, September, 2006)
"The book could be of interest to those applied mathematicians who feel that such material could be useful to them. . is intended to be a classroom text, in which each chapter is followed by an extensive 'Comments' section containing some background as well as some additional results. . it is more suited as a scholarly introduction to convex functions and their many uses. It very much lives up to its subtitle, A Contemporary Approach." (Robert Phelps, SIAM Review, Vol. 49 (1), 2007)
